The ratio of the area of square to that of the square drawn on its diagonal is:
(A)1:3
(B)3:4
(C)2:3
(D)1:2

April 3rd 2009, 06:51 AM

ADARSH

Quote:

Originally Posted by rickymylv

please tell me how to solve this problem

The ratio of the area of square to that of the square drawn on its diagonal is:
(A)1:3
(B)3:4
(C)2:3
(D)1:2

Let x be the side of square (all sides equal)

Length of its diagonal in terms of x = ?? ( Use Pythagoras theorem)
-----------------------------------
Area of square = (side)^2

Now solve it ! (Wait)

April 3rd 2009, 07:28 AM

Chop Suey

Given a square with sides of length s, the length of the diagonal of the square is equal to

The question asks for the ratio of the area of a square to the area of a square drawn on its diagonal. As in:

April 3rd 2009, 07:35 AM

Soroban

Hello, rickymylv!

Quote:

Please tell me how to solve this problem

The ratio of the area of a square to that of the square drawn on its diagonal is:

. .

A sketch is essential . . .

Code:

* - - - - - *
| |
| |
| | s
| |
| |
* - - - - - *
s

A square with side has area

Code:

* - - - - - *
| _ * |
| √2s * |
| * | s
| * |
| * |
* - - - - - *
s

The diagonal of the square can be found with Pythagorus:

. .

The area of the square of side is: .

Therefore, the ratio of the two areas is . . .

April 3rd 2009, 09:35 AM

lebanon

hello

let the side of the square be (a),so the area of the first square is a^2,
then by pythegoras , it's diagonal is a√2,and the area of the second square ia (a√2)^2=2(a^2).
therefore the ratio is:a^2 / 2(a^2)=1/2
D is correct.